Question

The first Lemoine circle is the circumcircle of one of these shapes. Pascal’s theorem describes the intersection of this shape’s sides when inscribed in a conic section. (-5[1])“Three root three over two times side length squared” (-5[1])gives the area for a regular one of these shapes. This shape is the least-sided polygon that does not form the faces of a platonic solid. (15[1])Only squares, triangles, and (*) these shapes tessellate the plane. Placing two isosceles trapezoids along their longest side will create these shapes. (10[1])These shapes contain internal angles of 120 degrees each, which sum to 720 degrees. For 10 points, name this polygon with six sides. ■END■ (10[1])

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